General theorems on rates of convergence in distribution of random variables II. Applications to the stable limit laws and weak law of large numbers

DOI10.1016/0047-259X(78)90072-6zbMath0383.60025MaRDI QIDQ1248836

L. Hahn, Paul L. Butzer

Publication date: 1978

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Sums of independent random variables; random walks (60G50) Rate of convergence, degree of approximation (41A25)

Related Items (14)

On the weak laws of large numbers for compound random sums of independent random variables with convergence rates ⋮ The generalized Trotter operator and weak convergence of dependent random variables in different probability metrics ⋮ General theorems on Little-\(\mathcal O\) rates of closeness of two weighted sums of independent Hilbert space valued random variables with applications ⋮ Invariant scale matrix hypothesis tests under elliptical symmetry ⋮ Approximation by operators of probabilistic type ⋮ On the rate of approximation in the central limit theorem for dependent random variables and random vectors ⋮ Invariant tests for the equality of k scale parameters under spherical symmetry ⋮ Unnamed Item ⋮ Approximation of stable law in Wasserstein-1 distance by Stein's method ⋮ On the rates of convergence in central limit theorems for compound random sums of independent random variables ⋮ General theorems on rates of convergence in distribution of random variables I. General limit theorems ⋮ Two-sided bounds on the rate of convergence to a stable law ⋮ On rates of convergence to infinitely divisible laws for dependent random variables ⋮ On the \(L_ p\) norm for some approximation operators

Cites Work

• On the rate of approximation in the central limit theorem
• Density versions of the univariate central limit theorem
• General theorems on rates of convergence in distribution of random variables I. General limit theorems
• Multivariate stable distributions
• On the Connections Between the Rates of Norm and Weak Convergence in the Central Limit Theorem
• Absolute Estimates of the Rate of Convergence to Stable Laws
• Convergence Rates in the Law of Large Numbers
• A Note on Convergence of Moments
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